An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be
a 200-meter single-lane running track.
(a) Draw a diagram that illustrates the problem. Let x and y represent the length and width of the rectangular region,
respectively.
(b) Determine the radius r, in terms of y, of the semicircular ends of the track.
r =____
Determine the distance d, in terms of y, around the inside edge of the two semicircular parts of the track.
d =____
(c) Use the result of part (b) to write an equation, in terms of x and y, for the distance traveled in one lap around the
track. Solve for y.
y =____
(d) Use the result of part (c) to write the area A of the rectangular region as a function of x.
A =____
(e) Use a graphing utility to graph the area function from part (d). Use the graph to approximate the dimensions that will
produce a rectangle of maximum area. (Round your answers to two decimal places.)
X =______m
y =______m
